Question

Ruby invested $850 in an account paying an interest rate of 2% compounded

quarterly. Logan invested $850 in an account paying an interest rate of 2%
compounded monthly. After 17 years, how much more money would Ruby have in
her account than Logan, to the nearest dollar?

Answer 1

Answer: $111

Explanation:

Answer 2

To the nearest dollar, Logan would have $1 in his account more than Ruby

Explanation:

Compound Interest

It occurs when the interest is reinvested rather than paying it out.

Interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

`\displaystyle A=P\left(1+{\frac {r}{n}}\right)^(nt)`

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Ruby invested P=$850 at r=2%=0.02 compounded quarterly. There are 4 quarts in a year, thus n=4. The investment lasted for t=17 years.

The final amount Ruby has is:

`\displaystyle A=850\left(1+{\frac {0.02}{4}}\right)^(4*17)`

A=850*1.40376

A=$1,193.19

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Logan invested P=$850 at r=2%=0.02 compounded monthly. There are 12 months in a year, thus n=12. The investment lasted for t=17 years.

The final amount Logan has is:

`\displaystyle A=850\left(1+{\frac {0.02}{12}}\right)^(12*17)`

A=850*1,40455

A=$1,193.87

The difference is $0.67.

To the nearest dollar, Logan would have $1 in his account more than Ruby